factoring - difference of squares
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Factoring - Difference of Squares. What is a Perfect Square. What numbers are Perfect Squares?. Squares. Perfect Squares. 1 4 9 16 25 36 49 64 81 100. Factoring: Difference of Squares. Count the number of terms. Is it a binomial? Is the first term a perfect square? - PowerPoint PPT PresentationTRANSCRIPT
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Factoring - Difference of Squares
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What is a Perfect Square
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What numbers are Perfect Squares?
Squares
1 12 2 42 3 92 4 162 5 252 6 362
Perfect Squares
149162536496481100 10
8
6
4
2
x
x
x
x
x
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Factoring: Difference of Squares
Count the number of terms. Is it a binomial?
Is the first term a perfect square?
Is the last term a perfect square?
Is it, or could it be, a subtraction of two perfect squares?
x2 – 9 = (x + 3)(x – 3)
The sum of squares will not factor a2+b2
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Using FOIL we find the product of two binomials.
)5)(5( xx
2x x5 x5 25252 x
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Rewrite the polynomial as the product of a sum and a difference.
)5)(5( xx252 x
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Conditions for Difference of Squares
Must be a binomial with subtraction. First term must be a perfect square.
(x)(x) = x2
Second term must be a perfect square (6)(6) = 36
362 x
66 xx
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Check for GCF.
Sometimes it is necessary to remove the GCF before it can be factored more completely.
22 455 yx 22 95 yx
yxyx 335
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Removing a GCF of -1.
In some cases removing a GCF of negative one will result in the difference of squares.
162 x
161 2 x
441 xx
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Difference of Squares
254 2 x
82 2 x1002 b
162 y
5252 xx
42 2 x 222 xx
PRIME! GCF. No
square.perfect anot 1st.
1001 2 b
44 yy
You Try
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Factoring - Difference of Squares